Codebook sub-sampling for CSI feedback on PUCCH for 4TX MIMO

ABSTRACT

Channel state information (CSI) feedback in a wireless communication system is disclosed. User equipment transmits a CSI feedback signal via a Physical Uplink Control Channel (PUCCH). If the UE is configured in a first feedback mode, the CSI comprises a first report jointly coding a Rank Indicator (RI) and a first precoding matrix indicator (PMI1), and a second report coding Channel Quality Indicator (CQI) and a second precoding matrix indicator (PMI2). If the UE is configured in a second feedback mode, the CSI comprises a first report coding RI, and a second report coding CQI, PMI1 and PMI2. The jointly coded RI and PMI1 employs codebook sub-sampling, and the jointly coding PMI1, PMI2 and CQI employs codebook sub-sampling.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of application Ser. No. 15/853,430filed Dec. 22, 2017, which is a continuation of application Ser. No.15/222,452, filed Jul. 28, 2016, now U.S. Pat. No. 9,853,703, which is acontinuation of application Ser. No. 14/831,698 filed Aug. 20, 2015, nowU.S. Pat. No. 9,407,346, which is a divisional of application Ser. No.14/187,216 filed Feb. 21, 2014, now U.S. Pat. No. 9,143,212, whichclaims the benefit of the filing dates of U.S. Provisional PatentApplication No. 61/768,857, filed on Feb. 25, 2013; U.S. ProvisionalPatent Application No. 61/815,081, filed on Apr. 23, 2013; U.S.Provisional Patent Application No. 61/823,663, filed on May 15, 2013;U.S. Provisional Patent Application No. 61/826,137, filed on May 22,2013; U.S. Provisional Patent Application No. 61/828,072, filed on May28, 2013, the disclosures of all of which are hereby incorporated byreference herein in their entirety.

TECHNICAL FIELD

The technical field of this invention is wireless communication such aswireless telephony.

BACKGROUND

The present embodiments relate to wireless communication systems and,more particularly, to the precoding of Physical Downlink Shared Channel(PDSCH) data and the associated demodulation reference signals withcodebook-based feedback for multi-input multi-output (MIMO)transmissions.

With Orthogonal Frequency Division Multiplexing (OFDM), multiple symbolsare transmitted on multiple carriers that are spaced apart to provideorthogonality. An OFDM modulator typically takes data symbols into aserial-to-parallel converter, and the output of the serial-to-parallelconverter is considered as frequency domain data symbols. The frequencydomain tones at either edge of the band may be set to zero and arecalled guard tones. These guard tones allow the OFDM signal to fit intoan appropriate spectral mask. Some of the frequency domain tones are setto values which will be known at the receiver. Among these are ChannelState Information Reference Signals (CSI-RS) and Dedicated orDemodulation Reference Signals (DMRS). These reference signals areuseful for channel estimation at the receiver.

In multi-input multi-output (MIMO) communication systems with multipletransmit/receive antennas, the data transmission is performed viaprecoding. Here, precoding refers to a linear (matrix) transformation ofL-stream data into P-stream where L denotes the number of layers (alsotermed the transmission rank) and P denotes the number of transmitantennas. With the use of dedicated (i.e. user-specific) DMRS, atransmitter, such as a base station or eNB (eNB), can perform precodingoperations that are transparent to user equipment (UE) acting asreceivers. It is beneficial for the base station to obtain a precodingmatrix recommendation from the user equipment. This is particularly thecase for frequency-division duplexing (FDD) where the uplink anddownlink channels occupy different parts of the frequency bands, i.e.the uplink and downlink are not reciprocal. Hence, a codebook-basedfeedback from the UE to the eNB is preferred. To enable a codebook-basedfeedback, a precoding codebook needs to be designed.

The 3GPP Long-Term Evolution (LTE) specification includes codebooks for2-antenna, 4-antenna, and 8-antenna transmissions. While those codebooksare designed efficiently, the present inventors recognize that stillfurther improvements in downlink (DL) spectral efficiency are possible.Accordingly, the preferred embodiments described below are directedtoward these problems as well as improving upon the prior art.

SUMMARY

Systems and methods for channel state information (CSI) and precodingmatrix indicator (PMI) feedback in a wireless communication system aredisclosed. A precoding matrix is generated for multi-antennatransmission based on a precoding matrix indicator (PMI) feedback fromat least one remote receiver wherein the PMI indicates a choice ofprecoding matrix derived from a matrix multiplication of two matricesfrom a first codebook and a second codebook, respectively. One or morelayers of a data stream are precoded with the precoding matrix andtransmitted to the remote receiver.

In one embodiment, Channel state information (CSI) feedback istransmitted by user equipment in a wireless communication system. Theuser equipment transmits a CSI feedback signal via a Physical UplinkControl CHannel (PUCCH). If the UE is configured in a first feedbackmode, the CSI comprises a first report jointly coding a Rank Indicator(RI) and a first precoding matrix indicator (PMI1), and a second reportcoding Channel Quality Indicator (CQI) and a second precoding matrixindicator (PMI2). If the UE is configured in a second feedback mode, theCSI comprises a first report coding RI, and a second report coding CQI,PMI1 and PMI2. The jointly coding RI and PMI1 employs codebooksub-sampling, and the jointly coding PMI1, PMI2 and CQI employs codebooksub-sampling. If submode 1 is selected RI and W1 are jointly encodedusing codebook sub sampling in report 1. If submode 2 is selected W1 andW2 are jointly encoded using codebook sub sampling in report 2.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of this invention are illustrated in thedrawings, in which:

FIG. 1 illustrates an exemplary wireless telecommunications network 100.

FIG. 2 is a flowchart illustrating a reporting process according to anexample embodiment.

FIG. 3 is a block diagram illustrating internal details of a mobile UEand an eNB in an exemplary network system.

FIGS. 4A-4C (“FIG. 4”) illustrate the time domain report sequences forPUCCH mode 1-1 submode 1, PUCCH mode 1-1 submode 2, and PUCCH mode 2-1.

DETAILED DESCRIPTION

The invention(s) now will be described more fully hereinafter withreference to the accompanying drawings. The invention(s) may, however,be embodied in many different forms and should not be construed aslimited to the embodiments set forth herein. Rather, these embodimentsare provided so that this disclosure will be thorough and complete, andwill fully convey the scope of the invention(s) to a person of ordinaryskill in the art. A person of ordinary skill in the art may be able touse the various embodiments of the invention(s).

FIG. 1 illustrates an exemplary wireless telecommunications network 100.Network 100 includes a plurality of base stations 101, 102 and 103. Inoperation, a telecommunications network necessarily includes many morebase stations. Each base station 101, 102 and 103 (eNB) is operable overcorresponding coverage areas 104, 105 and 106. Each base station'scoverage area is further divided into cells. In the illustrated network,each base station's coverage area is divided into three cells 104 a-c,105 a-c, 106 a-c. User equipment (UE) 107, such as telephone handset, isshown in Cell A 104 a. Cell A 104 a is within coverage area 104 of basestation 101. Base station 101 transmits to and receives transmissionsfrom UE 107. As UE 107 moves out of Cell A 104 a and into Cell B 105 b,UE 107 may be handed over to base station 102. Because UE 107 issynchronized with base station 101, UE 107 can employ non-synchronizedrandom access to initiate handover to base station 102.

Non-synchronized UE 107 also employs non-synchronous random access torequest allocation of uplink 108 time or frequency or code resources. IfUE 107 has data ready for transmission, which may be traffic data,measurements report, tracking area update, UE 107 can transmit a randomaccess signal on uplink 108. The random access signal notifies basestation 101 that UE 107 requires uplink resources to transmit the UEsdata. Base station 101 responds by transmitting to UE 107 via downlink109, a message containing the parameters of the resources allocated forUE 107 uplink transmission along with a possible timing errorcorrection. After receiving the resource allocation and a possibletiming advance message transmitted on downlink 109 by base station 101,UE 107 optionally adjusts its transmit timing and transmits the data onuplink 108 employing the allotted resources during the prescribed timeinterval.

Base station 101 configures UE 107 for periodic uplink SoundingReference Signal (SRS) transmission. Base station 101 estimates uplinkchannel state information (CSI) from the SRS transmission. The preferredembodiments of the present invention provide improved communicationthrough precoded multi-antenna transmission with codebook-basedfeedback. In a cellular communication system, a UE is uniquely connectedto and served by a single cellular base station or eNB at a given time.An example of such a system is the 3GPP LTE system, which includes theLTE-Advanced (LTE-A) system. With an increasing number of transmitantennas at the eNB, the task of designing an efficient codebook withdesirable properties is challenging.

For downlink data transmission in a cellular communication system, a UEmeasures the downlink wireless channel via downlink reference signalsand reports the measured Channel State Information (CSI) to the eNB. TheeNB utilizes the CSI report to perform downlink link adaptation andscheduling to determine data transmission schemes to the UE, includingbut not limited to time/frequency resource assignment, modulation andcoding schemes. The reference signals used by UE for channel estimationcan be cell-specific reference signal (CRS) or Channel-State-InformationReference Signals (CSI-RS) in LTE. CSI is reported in the form of a setof recommended MIMO transmission properties to the eNB. CSI consists ofChannel Quality Indicator (CQI), precoding matrix indicator (PMI),precoding type indicator (PTI), and/or rank indication (RI). RIindicates the number of data layers that the UE recommends the eNB totransmit. PMI is the index to a recommended precoding matrix in apre-determined codebook known to the eNB and the UE in advance. CQIreflects the channel quality that the UE expects to experience if therecommended RI/PMI is used for data transmission. The time and frequencyresources that can be used by the UE to report CSI are controlled by theeNB. A UE is semi-statically configured by higher layers to periodicallyfeedback different CSI components (CQI, PMI, PTI, and/or RI) on thePhysical Uplink Control CHannel (PUCCH). Different PUCCH modes can beconfigured for CSI feedback.

In one embodiment, a dual-stage codebook for CSI feedback is based onthe product structure proposed in:W=W ₁ W ₂  (1)where W1 targets wideband/long-term channel properties and W2 targetsfrequency-selective/short-term channel properties. Each of thecomponents W1, W2 is assigned a codebook. Hence, two distinct codebooksare needed: CB₁ and CB₂. W is termed the composite precoder. The choiceof W1 and W2 are indicated via PMI₁ and PMI₂, respectively.

The LTE Release 8 4Tx codebook is used for channel feedback to a4-antenna base station and is designed using the Householder structure,wherein a codebook of rank r (r=1, 2, 3, 4) comprises sixteen precodingmatrices that incur 4-bits of feedback overhead. For LTE Release 12, the4Tx codebook may be enhanced to a larger codebook size. In order toavoid substantially increasing the feedback overhead, the LTE Release 124Tx codebook may be enhanced using a double codebook structure such asused in the codebook adopted for 8Tx MIMO in LTE Release 10, whereineach precoding matrix is expressed as W=W1W2. Herein W denotes thecomposite precoding matrix, W1 is a wideband first precoding matrixcorresponding to a wideband/long-term channel property, and W2 is anarrow-band second precoding matrix corresponding to ashort-term/narrow-band channel property. Because W1 needs to be reportedonly once for the entire system bandwidth, the feedback overhead can beeffectively limited even if the composite codebook (W) size issubstantially larger than the LTE Release 8 codebook. In addition, as W1reflects the long-term channel characteristics, it can be fed back at asubstantially lower rate than W2 that targets the short-term channelproperty.

The enhanced 4Tx codebook in LTE Release 12 is designed with thedouble-codebook structure. For rank-1/2, both W1 and W2 codebook are ofsize 4-bit comprises sixteen precoders. For rank-3/4, Rel.8 codebook isreused such that the W1 codebook comprises a single 4×4 identity matrix,and the W2 codebook reuses the Rel.8 codebook, i.e. 16 precoders perrank. As such, the total payload of W1+W2 are 8/8/4/4 bits forrank-1/2/3/4. Since the maximum PUCCH payload is 11 bits, codebooksub-sampling needs to be implemented in order to meet the PUCCH payloadlimitation. This disclosure outlines codebook sub-sampling mechanisms inrelation to PUCCH mode 1-1, for submode 1 and submode 2, and PUCCH mode2-1.

Submode 1: W1 and W2 are reported in different time instances (e.g., indifferent subframes).

Submode 2: W1 and W2 are reported in the same time instances (e.g., inthe same subframe).

Table 1 is a reporting structure for PUCCH mode 1-1. Table entrieshaving the form x+y indicate the possibility for joint encoding. EachCSI report, report 1 or report 2, is transmitted over one PUCCH in onesubframe of 1 ms duration. The maximum payload of PUCCH is 11-bit; henceany CSI feedback on PUCCH should not exceed the 11-bit payloadlimitation. The total CSI payload depends on the contents of CSIreported on the PUCCH, e.g. RI, W1, W2, CQI or a combination thereof.For 4Tx MIMO channel, the maximum rank (RI) reported by the UE is 2 fora UE capable of maximum 2-layer data communication, and 4 for a UEcapable of maximum 4-layer data communication. Hence, the RI bit-widthis 1-bit or 2-bit, for UE capable of 2-layer or 4-layer communication,respectively. The CQI bit-width is a function of PUCCH mode and the RI.If RI=1, the UE reports one CQI for single layer data communication,using 4-bit. For RI greater than 1, the UE reports two CQIs for two datacodewords. The first CQI for the first codeword has 4-bits, and the CQIfor the second codeword is encoded differentially with respect to theCQI of the first codeword using 3-bits. Hence, the total CQI overhead is4-bits for RI=1 and 7-bits for RI>1. The bit-width for W1 and W2 dependson the codebook size, and may be different for different ranks. Forinstance, if the un-sub-sampled W1 codebook is 4-bit and theun-sub-sampled W1 codebook is 4-bit, the total payload of CQI+W1+W2without codebook sub-sampling is 7+8=15 bits for report 2 of PUCCH mode1-1 submode 2, exceeding the 11-bit PUCCH payload. Hence, codebooksub-sampling is required where the UE performs PMI selection within asub-sampled codebook of smaller-size, instead of the full 4-bit W1 and4-bit W2 codebook.

TABLE 1 Submode 1 Submode 2 Report 1 RI + W1 RI Report 2 CQI, W2 CQI,W1 + W2

The following is apparent from Table 1. For submode 1, report 2 simplyfollows the LTE Release 8 PMI principle where W2 is analogous to the LTERelease 8 PMI. Hence, there is no need to perform codebook sub-sampling,unless the payload associated with W2 exceeds 4-bits. For submode 2,report 1 carries only the LTE Release 8 RI. Hence, codebook sub-samplingis irrelevant here. Codebook sub-sampling is needed for Submode 1/Report1 and Submode 2/Report 2. This is discussed below.

FIG. 2 is a flowchart illustrating a reporting process according to anexample embodiment. FIG. 2 begins with start block 201. Test block 202determines if PUCCH mode 1-1 submode 1, PUCCH mode 1-1 submode 2, orPUCCH mode 2-1 is selected. If PUCCH mode 1-1 submode 1 is selected,then block 203 generates report 1 and RI and W1 are jointly encoded.They are also codebook sub-sampled according to one of the tables below.Block 204 generates report 2 with CQI and W2 separately encoded. Thetime domain reporting sequence of PUCCH mode 1-1 submode 1 isillustrated in FIG. 4A.

If PUCCH mode 1-1 submode 2 is selected in block 202, then block 205generates report 1. This includes the separately encoded RI. Block 206generates report 2 with CQI, W1 and W2. W1 and W2 are jointly encodedwith codebook sub-sampling according to one of the tables below. Thetime domain reporting sequence of PUCCH mode 1-1 submode 2 isillustrated in FIG. 4B.

If PUCCH mode 2-1 is selected in block 202, then block 207 generatesreport 1 comprising RI and a precoding type indicator (PTI). The valueof PTI is checked in block 209. If PTI=0, then block 210 generatesreport 2 comprising a wideband W1, and block 211 generates report 3comprising a wideband W2 and CQI. If PTI=1 in block 209, then block 212generates report 2 comprising a wideband W2 and CQI, and block 213generates a subband W2, subband CQI and a band indicator indicating theposition of the subband. Subband W2, subband CQI and subband indicatorare encoded with W2 codebook sub-sampling according to of the tablesbelow. The time domain reporting sequence of PUCCH mode 2-1 isillustrated in FIG. 4C.

FIG. 2 ends with continue block 213.

Codebook Enhancement.

An enhanced 4Tx codebook that can be used with this reporting structureis disclosed in pending U.S. patent application Ser. No. 14/177,547entitled “4TX Codebook Enhancement in LTE,” filed Feb. 11, 2014, thedisclosure of which is hereby incorporated by reference herein in itsentirety.

Details of the proposed codebook enhancements can be found in U.S.application Ser. No. 14/177,547, wherein the LTE Release 8 codebook isaugmented by enhanced codebook components designed according to theGrid-of-Beam (GoB) structure. For reference, the codebooks proposed inU.S. application Ser. No. 14/177,547 are re-captured below, which willbe used for the PUCCH sub-sampling discussion below.

With the GoB component, each precoder W is denoted as W=W1W2.

Precoding subspace for W1 is over-sampled by N discrete Fouriertransform (DFT) beams.

Each wideband W1 comprises Nb adjacent or non-adjacent beams to cover aspecific angle of departure (AoD) and angular spread. Different W1matrices may or may not have overlapping Nb/2 DFT beams.

Narrowband W2 performs beam selection and co-phasing.

For a GoB codebook without overlap, the following matrices are given inorder to describe the codebook:

$\begin{matrix}{\mspace{79mu}{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{N - 1}\end{bmatrix}}} & (1) \\{\mspace{79mu}{{\lbrack B\rbrack_{{1 + m},{1 + n}} = e^{J\frac{2\pi\; m\; n}{N}}},{m = 0},{{1\mspace{14mu} n} = 0},1,\ldots\mspace{14mu},{N - 1}}} & (2) \\{X^{(k)} \in \left\{ {{{\left\lfloor {b_{{({N_{b}k})}mod\ N}\ b_{{({{N_{b}k} + 1})}mod\ N}\mspace{14mu}\ldots\ b_{{({{N_{b}k} + N_{b} - 1})}{mod}\mspace{14mu} N}} \right\rfloor:k} = 0},{{\ldots\mspace{20mu}{N/N_{b}}} - 1}} \right\}} & (3)\end{matrix}$

For a GoB codebook with overlap, the following matrices are given inorder to describe the codebook:

$\begin{matrix}{\mspace{79mu}{B = \left\lbrack {b_{0}\mspace{20mu} b_{1}\mspace{14mu}\ldots\ b_{N - 1}} \right\rbrack}} & (4) \\{\mspace{79mu}{{\lbrack B\rbrack_{{1 + m},{1 + n}} = e^{j\frac{2\pi\; m\; n}{N}}},{m = 0},{{1\mspace{14mu} n} = 0},1,\ldots\mspace{14mu},{N - 1}}} & (5) \\{X^{(k)} \in \left\{ {{{\left\lfloor {b_{{{({N_{b}k})}/2}mod\ N}\ b_{{({{N_{b}{k/2}} + 1})}mod\ N}\mspace{14mu}\ldots\mspace{20mu} b_{{({{N_{b}{k/2}} + {N_{b}1}})}mod\ N}} \right\rfloor:k} = 0},{{\ldots\mspace{14mu} 2{N/N_{b}}} - 1}} \right\}} & (6)\end{matrix}$

Enhanced Codebook 1.

In one embodiment, the LTE Release 8 4Tx codebook is augmented by GoBcomponents of (N,Nb)=(16,4), without adjacent W1 overlapping.

Rank-1:

$\begin{matrix}{{W_{1} \in C_{1}} = {\left\{ {I_{4},\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix},\begin{bmatrix}X^{(1)} & 0 \\0 & X^{(1)}\end{bmatrix},\begin{bmatrix}X^{(2)} & 0 \\0 & X^{(2)}\end{bmatrix},\begin{bmatrix}X^{(3)} & 0 \\0 & X^{(3)}\end{bmatrix}} \right\}->{{size}\text{-}5\mspace{14mu}{\left( {{LTE}\mspace{14mu}{Release}\mspace{14mu} 8\mspace{14mu}{codebook}\mspace{14mu}{augmented}\mspace{14mu}{with}\mspace{14mu}{block}\mspace{14mu}{diagonal}\mspace{14mu}{GoB}} \right).}}}} & (7)\end{matrix}$

When W₁=I₄: W₂ ∈C_(2,R8Tx4r1), where C_(2,R8Tx4r1) denotes the LTERelease 8 4Tx rank-1 codebook used for W2.

$\begin{matrix}{\mspace{79mu}{{{When}\mspace{14mu} W_{1}} = {{\begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}\mspace{14mu}\left( {{k = 0},1,2,3} \right)}:}}} & \; \\{{{W_{2} \in {CB_{2}}} = \left\{ {{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\{jY}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\{- {jY}}\end{bmatrix}}} \right\}},} & (8) \\{\mspace{79mu}{Y \in \left\{ {\begin{bmatrix}1 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\1 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\0 \\1\end{bmatrix}} \right\}}} & (9)\end{matrix}$

Rank2:

$\begin{matrix}{{W_{1} \in C_{1}} = \left\{ {I_{4},\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix},\begin{bmatrix}X^{(1)} & 0 \\0 & X^{(1)}\end{bmatrix},\begin{bmatrix}X^{(2)} & 0 \\0 & X^{(2)}\end{bmatrix},\begin{bmatrix}X^{(3)} & 0 \\0 & X^{(3)}\end{bmatrix}} \right\}} & (10)\end{matrix}$

-   -   → size-5 (LTE Release 8 codebook augmented with block diagonal        GoB).

When W₁=I₄: W₂ ∈ C_(2,R8Tx4r2) where C_(2,R8Tx4r2) denotes the LTERelease 8 4Tx rank-2 codebook used for W2.

$\begin{matrix}{\mspace{79mu}{{{When}\mspace{14mu} W_{1}} = {\begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}\mspace{14mu}\left( {{k = 0},1,2,3} \right)\text{:}}}} & \; \\{\mspace{79mu}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (11) \\{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1}^{4},e_{1}^{4}} \right),\left( {e_{2}^{4},e_{2}^{4}} \right),\left( {e_{3}^{4},e_{3}^{4}} \right),\left( {e_{4}^{4},e_{4}^{4}} \right),\left( {e_{1}^{4},e_{2}^{4}} \right),\left( {e_{2}^{4},e_{3}^{4}} \right),\left( {e_{1}^{4},e_{4}^{4}} \right),\left( {e_{2}^{4},e_{4}^{4}} \right)} \right\}} & (12)\end{matrix}$

For Rank-3 and Rank-4, reuse the LTE Release 8 codebook.

This design can be extended to include adjacent overlapping W1:

Rank1:

$\begin{matrix}{{W_{1} \in C_{1}} = \left\{ {I_{4},\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix},\ldots\mspace{14mu},\begin{bmatrix}X^{(7)} & 0 \\0 & X^{(7)}\end{bmatrix}} \right\}} & (13)\end{matrix}$

Rank2:

$\begin{matrix}{{W_{1} \in C_{1}} = \left\{ {I_{4},\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix},\ldots\mspace{14mu},\begin{bmatrix}X^{(7)} & 0 \\0 & X^{(7)}\end{bmatrix}} \right\}} & (14)\end{matrix}$

where the C2 codebook remains the same.

Enhanced Codebook 2.

In one embodiment, the LTE Release 8 4-Tx codebook is augmented by GoBcomponents of (N,Nb)=(16,4), without adjacent W1 overlapping. The LTERelease 8 4Tx codebook is not included in the LTE Release 12 4Txcodebook.

Rank-1:

$\begin{matrix}{{W_{1} \in C_{1}} = {\left\{ {\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix},\begin{bmatrix}X^{(1)} & 0 \\0 & X^{(1)}\end{bmatrix},\begin{bmatrix}X^{(2)} & 0 \\0 & X^{(2)}\end{bmatrix},\begin{bmatrix}X^{(3)} & 0 \\0 & X^{(3)}\end{bmatrix}} \right\}->\mspace{79mu}{{size}\text{-}4}}} & (15)\end{matrix}$

When

$W_{1} = {{\begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}\mspace{14mu}\left( {{k = 0},1,2,3} \right)}:}$

$\begin{matrix}{{{W_{2} \in {CB_{2}}} = \left\{ {{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\{jY}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\{- {jY}}\end{bmatrix}}} \right\}},} & (16) \\{\mspace{79mu}{Y \in \left\{ {\begin{bmatrix}1 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\1 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\0 \\1\end{bmatrix}} \right\}}} & (17)\end{matrix}$

Rank 2:

$\begin{matrix}{{W_{1} \in C_{1}} = {\left\{ {\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix},\begin{bmatrix}X^{(1)} & 0 \\0 & X^{(1)}\end{bmatrix},\begin{bmatrix}X^{(2)} & 0 \\0 & X^{(2)}\end{bmatrix},\begin{bmatrix}X^{(3)} & 0 \\0 & X^{(3)}\end{bmatrix}} \right\}->\mspace{79mu}{{size}\text{-}4}}} & (18)\end{matrix}$

When

$W_{1} = {{\begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}\mspace{20mu}\left( {{k = 0},1,2,3} \right)}:}$

$\begin{matrix}{\mspace{79mu}{{{W_{2} \in {CB_{2}}} = \left\{ {{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (19) \\{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1}^{4},e_{1}^{4}} \right),\left( {e_{2}^{4},e_{2}^{4}} \right),\left( {e_{3}^{4},e_{3}^{4}} \right),\left( {e_{4}^{4},e_{4}^{4}} \right),\left( {e_{1}^{4},e_{2}^{4}} \right),\left( {e_{2}^{4},e_{3}^{4}} \right),\left( {e_{1}^{4},e_{4}^{4}} \right),\left( {e_{2}^{4},e_{4}^{4}} \right)} \right\}} & (20)\end{matrix}$

For Rank-3 and Rank-4, reuse the LTE Release 8 codebook.

This design may be extended to include adjacent overlapping W1:

Rank1:

$\begin{matrix}{{W_{1} \in C_{1}} = \left\{ {\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix},\ldots\mspace{14mu},\begin{bmatrix}X^{(7)} & 0 \\0 & X^{(7)}\end{bmatrix}} \right\}} & (21)\end{matrix}$

Rank2:

$\begin{matrix}{{W_{1} \in C_{1}} = \left\{ {\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix},\ldots\mspace{14mu},\begin{bmatrix}X^{(7)} & 0 \\0 & X^{(7)}\end{bmatrix}} \right\}} & (22)\end{matrix}$

The C2 codebook remains the same.

Enhanced Codebook 3.

In yet another embodiment, the rank-1 and rank-2 codebooks are the sameas enhanced codebook 1, while the rank-3 and rank-4 codebooks areenhanced using a (N,Nb)=(4,4) GoB structure.

Rank-3:

$\begin{matrix}{{W_{1} \in C_{1}} = \left. \left\{ {I_{4},\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix}} \right\}\rightarrow{{size} - {2\mspace{14mu}{\left( {{Rel}\text{-}8\mspace{14mu}{codebook}\mspace{14mu}{augmented}\mspace{14mu}{with}\mspace{14mu}{block}\mspace{14mu}{diagonal}\mspace{14mu}{GoB}} \right).}}} \right.} & (23)\end{matrix}$

When W₁=I₄: W₂ ∈ C_(2,R8Tx4r3) where C_(2,R8Tx4r3) denotes the LTERelease 8 4Tx rank-3 codebook used for W2.

When

$W_{1} = {\begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}\mspace{14mu}\left( {k = 0} \right)\text{:}}$

$\begin{matrix}{\mspace{79mu}{{{W_{2} \in {CB_{2}}} = \left\{ {{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (24) \\{\mspace{79mu}{and}} & \; \\{\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix}{\left( {e_{1}^{4},\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack} \right),\left( {e_{2}^{4},\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack} \right),\left( {e_{3}^{4},\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack} \right),\left( {e_{4}^{4},\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack} \right),} \\{\left( {\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack,e_{1}^{4}} \right),\left( {\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack,e_{2}^{4}} \right),\left( {\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack,e_{3}^{4}} \right),\left( {\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack,e_{4}^{4}} \right)}\end{Bmatrix}} & (25)\end{matrix}$

Rank-4:

$\begin{matrix}{{W_{1} \in C_{1}} = \left. \left\{ {I_{4},\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix}} \right\}\rightarrow{{Size}\text{-}2\mspace{14mu}{\left( {{Rel}\text{-}8\mspace{14mu}{codebook}\mspace{14mu}{augmented}\mspace{14mu}{with}\mspace{14mu}{block}\mspace{14mu}{diagonal}\mspace{14mu}{GoB}} \right).}} \right.} & (26)\end{matrix}$

When W₁=I₄: W₂∈ C_(2,R8Tx4r4) where C_(2,R8Tx4r4) denotes the LTERelease 8 4Tx rank-4 codebook used for W2.

When

$W_{1} = {\begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}\mspace{14mu}\left( {k = 0} \right)\text{:}}$

$\begin{matrix}{{{W_{2} \in {CB_{2}}} = \left\{ {{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},} & (27) \\{where} & \; \\{\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix}{\left( {\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack,\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack} \right),\left( {\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack,\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack} \right),} \\{\left( {\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack,\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack} \right),\left( {\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack,\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack} \right)}\end{Bmatrix}} & (28)\end{matrix}$

corresponding to i₁=0 . . . 7.

W2 can be reserved for i₂=8 . . . 15.

Enhanced Codebook 4.

In yet another embodiment, the rank-1 and rank-2 codebooks are the sameas enhanced codebook 2, while the rank-3 and rank-4 codebooks areenhanced using (N,Nb)=(4,4) GoB design.

Rank-3:

$\begin{matrix}{{W_{1} \in C_{1}} = \left. \left\{ {I_{4},\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix}} \right\}\rightarrow{{size}\text{-}2\mspace{14mu}{\left( {{Rel}\text{-}8\mspace{14mu}{codebook}\mspace{14mu}{augmented}\mspace{14mu}{with}\mspace{14mu}{block}\mspace{14mu}{diagonal}\mspace{14mu}{GoB}} \right).}} \right.} & (29)\end{matrix}$

When W₁=I₄: W₂ ∈ C_(2,R8Tx4r3) where C_(2,R8Tx4r3) denotes the LTERelease 8 4Tx rank-3 codebook used for W2.

When

$W_{1} = {\begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}\mspace{14mu}\left( {k = 0} \right)\text{:}}$

$\begin{matrix}{\mspace{79mu}{{{W_{2} \in {CB_{2}}} = \left\{ {{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (30) \\{\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix}{\left( {e_{1}^{4},\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack} \right),\left( {e_{2}^{4},\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack} \right),\left( {e_{3}^{4},\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack} \right),\left( {e_{4}^{4},\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack} \right),} \\{\left( {\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack,e_{1}^{4}} \right),\left( {\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack,e_{2}^{4}} \right),\left( {\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack,e_{3}^{4}} \right),\left( {\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack,e_{4}^{4}} \right)}\end{Bmatrix}} & (31)\end{matrix}$

Rank-4:

${W_{1} \in C_{1}} = \left\{ {I_{4},\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix}} \right\}$

→Size-2 (Rel-8 codebook augmented with block diagonal GoB).

When W₁=I₄:W₂∈ C_(2,R8Tx4r4) where C_(2,R8Tx4r4) denotes the LTE Release8 4Tx rank-4 codebook used for W2.

When

$W_{1} = {\begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}\mspace{14mu}\left( {k = 0} \right)\text{:}}$

$\begin{matrix}{{{W_{2} \in {CB_{2}}} = \left\{ {{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},\;{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},} & (33) \\{where} & \; \\{{\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix}{\left( {\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack,\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack} \right),\left( {\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack,\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack} \right),} \\{\left( {\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack,\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack} \right),\left( {\left\lbrack {e_{2}^{4},e_{4}^{4}} \right\rbrack,\left\lbrack {e_{1}^{4},e_{3}^{4}} \right\rbrack} \right)}\end{Bmatrix}},} & (34)\end{matrix}$

corresponding to =0 . . . 7.

W2 can be reserved for i₂=8 . . . 15.

Codebook Sub-Sampling Submode 1 (RI+W1)

In this case, the total payload RI+W1 is kept small to ensure that theeffect of error propagation is not significant for any practical rangeof RI reporting interval. Hence, the following actions are performed toattain this goal when sub-sampling is performed on the codebook C1 forW1:

-   -   Joint encoding of RI and W1;    -   W1=I₄ matrix should not be sub-sampled. In other words, the        sub-sampled W1 codebook (C1) shall comprise the 4×4 identity        matrix;    -   Overlapping beams between two different W1 matrices, if they        exist, can be skipped; and    -   Since precoding gain is expected to be small for higher-rank        transmission (rank>2), fixed precoding (using only one W1        matrix) should also be considered whenever appropriate. This        applies if the LTE Release 12 4Tx codebook does not re-use the        LTE Release 8 codebook for high ranks (e.g., rank 3 and 4).

Keeping the above principles in mind, three exemplary W1 codebooksub-sampling schemes are given below in the tables listed in thissection. The examples are ordered with the increasing total number ofhypotheses. Note that it is possible to combine a part of one examplewith other part(s) from other examples.

Sub-Sampling for Enhanced Codebook 1.

For the enhanced codebook 1 above, the following sub-sampling scheme isproposed.

Tables 2 and 3 illustrate a sub-sampling of codebook C1 for enhancedcodebook 1 above.

TABLE 2 Number of W1 RI Chosen W1 index for sub-sampling (i₁) hypotheses1 0, 1, 2, 3, 4, 5 2 0, 1, 2, 3, 4 5 3 0 (fixed precoding) 1 4 0 (fixedprecoding) 1 Total number of hypotheses across ranks: 10 → 4 bits for UEcapable of 2-layers 12 → 4 bits for UE capable of 4-layers

TABLE 3 Value of joint encoding of RI and the first PMI CodebookI_(RI/PMI1) RI index i₁ 0-7 1 2I_(RI/PMI1)  8-15 2 2(I_(RI/PMI1) − 8) 16 3 2(I_(RI/PMI1) − 16) 17 4 2(I_(RI/PMI1) − 17) 18-31 reserved NA

If W1 overlapping is introduced for the GoB components, the followingsub-sampling schemes are proposed.

Table 4 is a sub-sampling of codebook C1 for enhanced codebook 1 above,with W1 overlapping.

TABLE 4 Number of W1 RI Chosen W1 index for sub-sampling (i₁) hypotheses1 0, 1, 3, 5, 7, 5 2 0, 1, 3, 5, 7 5 3 0 (fixed precoding) 1 4 0 (fixedprecoding) 1 Total number of hypotheses across ranks: 10 → 4 bits for UEcapable of 2-layers 12 → 4 bits for UE capable of 4-layers

Alternatively the sub-sampled C1 codebook may replace codeword i_(t)=1,3, 5, 7 with i₁=2, 4, 6, 8, for either/both rank-1 and rank-2.

Sub-sampling for enhanced codebook 2.

For enhanced codebook 2, the following sub-sampling scheme is proposed.

Table 5 illustrates sub-sampling of codebook C1 for enhanced codebook 2.

TABLE 5 Number of W1 RI Chosen W1 index for sub-sampling (i₁) hypotheses1 0, 1, 2, 3 4 2 0, 1, 2, 3 4 3 0 (fixed precoding) 1 4 0 (fixedprecoding) 1 Total number of hypotheses across ranks: 8→ 3 bits for UEcapable of 2-layers 10 → 4 bits for UE capable of 4-layers

If W1 overlapping is introduced for the GoB components, the followingsub-sampling schemes are proposed.

Table 6 illustrates sub-sampling of codebook C1 for enhanced codebook 2with W1 overlapping.

TABLE 6 Number of W1 RI Chosen W1 index for sub-sampling (i₁) hypotheses1 0, 2, 4, 6 4 2 0, 2, 4, 6 4 3 0 (fixed precoding) 1 4 0 (fixedprecoding) 1 Total number of hypotheses across ranks: 8 → 3 bits for UEcapable of 2-layers 10 → 4 bits for UE capable of 4-layers

Alternatively the sub-sampled codebook C1 may replace codeword i₁=0, 2,4, 6 with i₁=1, 3, 5, 7, for either/both rank-1 and rank-2.

Sub-Sampling for Enhanced Codebook 3.

For enhanced codebook 3, the following sub-sampling scheme is proposed.

Table 7 illustrates sub-sampling of codebook C1, for enhanced codebook3.

TABLE 7 Number of W1 RI Chosen W1 index for sub-sampling (i₁) hypotheses1 0, 1, 2, 3, 4 5 2 0, 1, 2, 3, 4 5 3 0, 1, 2 4 0, 1 2 Total number ofhypotheses across ranks: 10→ 4 bits for UE capable of 2-layers 14 → 4bits for UE capable of 4-layers

If W1 overlapping is introduced for the GoB components, the followingsub-sampling schemes are proposed.

Table 8 illustrates sub-sampling of codebook C1 for enhanced codebook 3above with W1 overlapping.

TABLE 8 Number of W1 RI Chosen W1 index for sub-sampling (i₁) hypotheses1 0, 1, 3, 5, 7 5 2 0, 1, 3, 5, 7 5 3 0, 1, 2 4 0, 1 2 Total number ofhypotheses across ranks: 10→ 4 bits for UE capable of 2-layers 14 → 4bits for UE capable of 4-layers

Alternatively the sub-sampled C1 codebook may replace codeword i₁=1, 3,5, 7 with i₁=2, 4, 6, 8, for either/both rank-1 and rank-2.

Sub-Sampling for Enhanced Codebook 4.

For enhanced codebook 4, the following sub-sampling scheme is proposed.

Table 9 illustrates sub-sampling of codebook C1 for enhanced codebook 4.

TABLE 9 Number of W1 RI Chosen W1 index for sub-sampling (i₁) hypotheses1 0, 1, 2, 3 4 2 0, 1, 2, 3 4 3 0, 1, 2 4 0, 1 2 Total number ofhypotheses across ranks: 8→ 3 bits for UE capable of 2-layers 12 → 4bits for UE capable of 4-layers

If W1 overlapping is introduced for the GoB components, the followingsub sampling are proposed.

Table 10 illustrates sub-sampling of codebook C1 for enhanced codebook 4with W1 overlapping.

TABLE 10 Number of W1 RI Chosen W1 index for sub-sampling (i₁)hypotheses 1 0, 2, 4, 6 4 2 0, 2, 4, 6 4 3 0, 1, 2 4 0, 1 2 Total numberof hypotheses across ranks: 8→ 3 bits for UE capable of 2-layers 12 → 4bits for UE capable of 4-layers

Alternatively the sub-sampled C1 codebook may replace codeword i₁=0, 2,4, 6 with i₁==1, 3, 5, 7, for either/both rank-1 and rank-2.

For any of the above exemplary designs in Tables 2-10, it is possible tocombine a part of one example with other part(s) from other examples inTables 2-10.

Codebook Sub-Sampling Submode 2 (CQI, W1+W2).

In this case, the total payload of CQI together with W1+W2 should notexceed 11 bits to ensure the same worst-case coverage as the LTE Release8 PUCCH format 2/2a/2b. Hence, the following actions are performed toattain such goal when sub-sampling is performed on the codebook C1+C2for W1+W2:

To maintain the maximum PUCCH overhead of 11 bits:

-   -   RI=1: Since CQI occupies 4 bits, the payload for W1+W2 should        not exceed 7 bits, and    -   RI>1: Since CQI occupies 7 bits, the payload for W1+W2 should        not exceed 4 bits;    -   Joint encoding of W1 and W2 should be performed whenever        possible. This ensures efficient signaling of W1+W2 with minimum        overhead;    -   Overlapping beams between two different W1 matrices can be        skipped whenever appropriate as overlapping beam can be seen as        an optimization feature;    -   Since precoding gain is expected to be small for higher-rank        transmission (rank>4), fixed precoding (using only one W1        matrix) should also be considered whenever appropriate; and    -   Sub-sampling of C1 and C2 can also be performed jointly rather        than separately.

Keeping the above principles in mind, three exemplary W1+W2 codebooksub-sampling schemes are given below. Indices of W1 and W2 are given byi₁ and i₂ respectively.

Sub-Sampling for Enhanced Codebook 1.

Using the 4Tx codebook proposed as enhanced codebook 1, without W1overlapping, the following sub-sampling scheme is proposed.

Table 11 illustrates sub-sampling of codebook C1+C2, for enhancedcodebook 1 without W1 overlapping.

TABLE 11 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 Alternative 1: 16 + 4 * 16 = W1: 0, 1, 2, 3, 4, (i₁) 80 → 7bits W2: If W1 = identity matrix (i₁ = 0), no sub-sampling. (Note thiscorresponds to LTE Release 8 codebook.) Otherwise, for each W1 (i₁ = 1,2, 3, 4), choose Y = e₁, e₂, e₃, e₄ with all 4 possible co-phasing.(Note: this resembles (N, Nb) = (16, 1) design.) Alternative 2: 4 * 16 =64 → 6 bits W1: 1, 2, 3, 4, (i₁), corresponding to the enhancementprecoding matrices. (Note: this implies that LTE Release 8 codebook isnot used for PUCCH submode 1. This applies if the enhancement componentsof the LTE Release 12 codebook comprise of all 16 rank-1 LTE Release 8precoding vectors.) W2: For each W1 (i₁ = 1, 2, 3, 4), choose Y = e₁,e₂, e₃, e₄ with all 4 possible co-phasing. (Note this resembles (N, Nb)= (16, 1) design.) 2 Alternative 1: 4 bits W1: 0 (fixed precoding) (Notethis corresponds to LTE Release 8 codebook.) Alternative 2: 4 bits W1:i₁ = 1, 2, 3, 4. corresponding to the enhancement precoding matrices.W2: For each W1, choose only (Y₁, Y₂)=(e₁, e₁), (e₃, e₃) with all 2possible co-phasing. 3 W1: 0 (i₁ = 0) 4 bits W2: No sub-sampling. 4 W1:0 (i₁ = 0) 4 bits W2: No sub-sampling.

If overlapping between adjacent W1 matrices is introduced to the designof enhanced codebook 1, the following sub-sampling is proposed.

Table 12 illustrates sub-sampling of codebook C1+C2 for enhancedcodebook 1 with W1 overlapping.

TABLE 12 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 W1: 0, 1, 3, 5, 7, (i₁) 16 + 4 * 16 = W2: If W1 = identitymatrix (i₁ = 0), no 80 → 7 bits sub-sampling. (Note this corresponds toLTE Release 8 codebook.) Otherwise, for each W1 (i₁ = 1, 3, 5, 7),choose Y = e₁, e₂, e₃, e₄ with all 4 possible co-phasing. (Note thisresembles (N, Nb) = (16, 1) design.) 2 Alternative 1: 4 bits W1: i1 = 0(fixed precoding) (Note this corresponds to LTE Release 8 codebook.)Alternative 2: 4 bits W1: i₁ = 1, 3, 5, 7. corresponding to theenhancement precoding matrices. W2: For each W1, choose only (Y₁, Y₂) =(e₁, e₁), (e₃, e₃) with all 2 possible co-phasing. 3 W1: 0 4 bits W2: Nosub-sampling 4 W1: 0 4 bits W2: No sub-sampling

Sub-Sampling for Enhanced Codebook 2.

Using the 4Tx codebook proposed as enhanced codebook 2, without W1overlapping, the following sub-sampling scheme is proposed.

Table 13 illustrates sub-sampling of codebook C1+C2, for enhancedcodebook 2 without W1 overlapping.

TABLE 13 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 W1: 0, 1, 2, 3 (i₁) 4 * 16 = 64 → 6 bits W2: For each W1(i₁ = 0, 1, 2, 3), choose Y = e₁, e₂, e₃, e₄ with all 4 possibleco-phasing. (Note this resembles (N, Nb) = (16, 1) design.) 2 W1: i₁ =0, 1, 2, 3. 4 bits W2: For each W1, choose only (Y₁, Y₂) = (e₁, e₁),(e₃, e₃) with all 2 possible co-phasing. 3 W1: 0 4 bits W2: Nosub-sampling 4 W1: 0 4 bits W2: No sub-sampling

If overlapping between adjacent W1 matrices is introduced to the designof enhanced codebook 2, the following sub-sampling is proposed.

Table 14 illustrates sub-sampling of codebook C1+C2, for enhancedcodebook 2, with W1 overlapping.

TABLE 14 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 W1: 0, 2, 4, 6 (i₁) 4 * 16 = 64 → 6 bits W2: For each W1(i₁ = 0, 1, 2, 3), choose Y = e₁, e₂, e₃, e₄ with all 4 possibleco-phasing. (Note this resembles (N, Nb) = (16, 1) design.) 2 W1: i₁ =0, 2, 4, 6. 4 bits W2: For each W1, choose only (Y₁, Y₂) = (e₁, e₁),(e₃, e₃) with all 2 possible co-phasing. 3 W1: 0 4 bits W2: Nosub-sampling 4 W1: 0 4 bits W2: No sub-sampling

Sub-Sampling for Enhanced Codebook 3.

Using the 4Tx codebook proposed for enhanced codebook 3, without W1overlapping, the following sub-sampling scheme is proposed.

Table 15 illustrates sub-sampling of codebook C1+C2, for enhancedcodebook 3, without W1 overlapping.

TABLE 15 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 Alternative 1: 16 + 4 * 16 = W1: 0, 1, 2, 3, 4, (i₁) 80 → 7bits W2: If W1 = identity matrix (i₁ = 0), no sub-sampling. (Note thiscorresponds to LTE Release 8 codebook) Otherwise, for each W1 (i₁ = 1,2, 3, 4), choose Y = e₁, e₂, e₃, e₄ with all 4 possible co-phasing.(Note this resembles (N, Nb) = (16, 1) design.) Alternative 2: 4 * 16 =64 → 6 bits W1: 1, 2, 3, 4, (i₁), corresponding to the enhancementprecoding matrices W2: For each W1 (i₁ = 1, 2, 3, 4), choose Y = e₁, e₂,e₃, e₄ with all 4 possible co-phasing. (Note this resembles (N, Nb) =(16, 1) design.) 2 Alternative 1: 4 bits W1, i₁ = 0 (fixed precoding)(Note this correspond to LTE Release 8 codebook.) Alternative 2: 4 bitsW1: i₁ = 1, 2, 3, 4. W2: For each W1, choose only (Y₁, Y₂) = (e₁, e₁),(e₃, e₃) with all 2 possible co-phasing. 3 Alternative 1: W1: i₁ = 0. 4bits W2: No sub-sampling. Alternative 2: W1: i₁ = 1. 3 bits W2: Nosub-sampling. 4 Alternative 1: W1: i₁ = 0. 4 bits W2: No sub-sampling.Alternative 2: W1: i₁ = 1. 3 bits W2: No sub-sampling.

If overlapping between adjacent W1 matrices are introduced to the designof enhanced codebook 3, the following subsampling is proposed.

Table 16 illustrates sub-sampling of codebook C1+C2, for enhancedcodebook 3, with W1 overlapping.

TABLE 16 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 W1: 0, 1, 3, 5, 7, (i₁) 16 + 4 * 16 = W2: If W1 = identitymatrix (i₁ = 0), 80 → 7 bits no sub-sampling. Otherwise, for each W1 (i₁= 1, 3, 5, 7), choose Y = e_(1,) e₂, e₃, e₄ with all 4 possibleco-phasing. (Note this resembles (N, Nb) = (16, 1) design.) 2Alternative 1: 4 bits W1: 0 (fixed precoding). Alternative 2: 4 bits W1:i₁ = 1, 3, 5, 7, corresponding to the enhancement precoding matrices.W2: For each W1, choose only (Y₁, Y₂) = (e₁, e₁), (e₃, e₃) with all 2possible co-phasing. 3 Alternative 1: W1: i₁ = 0. 4 bits W2: Nosub-sampling. Alternative 2: W1: i₁ = 1. 3 bits W2: No sub-sampling. 4Alternative 1: W1: i₁ = 0. 4 bits W2: No sub-sampling. Alternative 2:W1: i₁ = 1. 3 bits W2: No sub-sampling.

Sub-Sampling for Enhanced Codebook 4.

Using the 4Tx codebook proposed as enhanced codebook 4, without W1overlapping, the following sub-sampling scheme is proposed.

Table 17 illustrates a sub-sampling of codebook C1+C2, for enhancedcodebook 4, without W1 overlapping.

TABLE 17 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 W1: 0, 1, 2, 3 (i₁) 4 * 16 = 64 → 6 bits W2: For each W1(i₁ = 0, 1, 2, 3), choose Y = e₁, e₂, e₃, e₄ with all 4 possibleco-phasing. (Note this resembles (N, Nb) = (16, 1) design.) 2 W1: i₁ =0, 1, 2, 3. 4 bits W2: For each W1, choose only (Y₁, Y₂) = (e₁, e₁),(e₃, e₃) with all 2 possible co-phasing. 3 Alternative 1: W1: i₁ = 0. 4bits W2: No sub-sampling. Alternative 2: W1: i₁ = 1. 3 bits W2: Nosub-sampling. 4 Alternative 1: W1: i₁ = 0. 4 bits W2: No sub-sampling.Alternative 2: W1: i₁ = 1. 3 bits W2: No sub-sampling.

If overlapping between adjacent W1 matrices is introduced to the designof enhanced codebook 4, the following subsampling is proposed.

Table 18 illustrates sub-sampling of codebook C1+C2, for enhancedcodebook 4, with W1 overlapping.

TABLE 18 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 W1: 0, 2, 4, 6 (i₁) 4 * 16 = 64 → 6 bits W2: For each W1(i₁ = 0, 1, 2, 3), choose Y = e₁, e₂, e₃, e₄ with all 4 possibleco-phasing. (Note this resembles (N, Nb) = (16, 1) design.) 2 W1: i₁ =0, 2, 4, 6. 4 bits W2: For each W1, choose only (Y₁, Y₂) = (e₁, e₂),(e₃, e₃) with all 2 possible co-phasing. 3 Alternative 1: W1: i₁ = 0. 4bits W2: No sub-sampling. Alternative 2: W1: i₁ = 1. 3 bits W2: Nosub-sampling. 4 Alternative 1: W1: i₁ = 0. 4 bits W2: No sub-sampling.Alternative 2: W1: i₁ = 1. 3 bits W2: No sub-sampling.

For any of the above exemplary designs in Tables 11-18, it is possibleto combine a part of one example with other part(s) from other examplesin other Tables 11-18.

Using 8Tx Sub-Sampling for 4Tx Feedback on PUCCH.

As discussed in the disclosure of U.S. application Ser. No. 14/177,547,the enhancement component of the proposed 4Tx codebook is designed withGoB principles. Note that the same GoB principle has been used in thedesign of LTE Release 10 8Tx codebook, where N=32 and Nb=4. It is notedthat the GoB design principle is universally applicable to manyTX-dimension (e.g., N_(t)=4, 8, 16, . . . ). As such, a 4Tx codebookdesigned with GoB can be derived by down-scaling the 8Tx GoB codebook,wherein downscaling refers to selecting four rows out of the eight rowsof an 8Tx precoding matrix. Several possibilities of codebookdownscaling have been discussed in U.S. application Ser. No. 14/177,547.For instance, the 4Tx codebook can be derived by downscaling allprecoding matrices of the 8Tx codebook, or that the 4Tx codebookcomprises of down-sized precoding matrices from a subset of the 8Txcodebook. In these two cases, 4Tx sub-sampling on PUCCH may be based onthe sub-sampling of 8Tx feedback in LTE Release 10.

In one embodiment, the 4Tx codebook (i.e., the enhancement componentcorresponding to GoB double-codebook structure) is derived bydownscaling all precoding matrices of the 8Tx codebook. This impliesthat the 4Tx codebook of the enhancement component is design with (N,Nb)=(32,4) and has the same codebook size as the 8Tx codebook, for bothW1 codebook C1, W2 codebook C2, as well as the composite codebook C.It's therefore possible to design 4Tx PUCCH sub-sampling based on 8TxPUCCH sub-sampling.

Rank-1/2

In one embodiment, the enhanced LTE Release 12 4Tx codebook iscompletely redesigned and comprises the down-scaled 8Tx precodingmatrices. The enhanced LTE Release 12 codebook does not comprise any LTERelease 8 codebook vectors. In such a case, 4Tx PUCCH sub-sampling mayreuse the same PUCCH feedback mechanism of 8Tx.

For a UE Capable of 2-Layer Operation:

For PUCCH submode 1, the sub-sampling illustrated in Tables 19 and 20can be used.

TABLE 19 Number of W1 RI Chosen W1 index for sub-sampling (i₁)hypotheses 1 Every other W1 matrix of the GoB 8 codebook, e.g. 0, 2, 4,6, 8, 10, 12, 14 2 Every other W2 matrix of the GoB 8 codebook, e.g. 0,2, 4, 6, 8, 10, 12, 14 Total number of hypotheses across ranks: 16 → 4bits for UE capable of 2-layers

TABLE 20 Value of joint encoding of RI and the first PMI CodebookI_(RI/PMI1) RI index i₁ 0-7  1 2I_(RI/PMI1) 8-15 2 2(I_(RI/PMI1) − 8)

For PUCCH submode 2, the sub-sampling illustrated in Tables 21 and 22can be used.

TABLE 21 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 W1: 0, 2, 4, 6, 8, 10, 12, 14 (i₁) 8 * 16 = 64 → 7 bits W2:For each W1 (i₁ = 0, 1, 2, 3), choose Y = e1, e2, e3, e4 with all 4possible co-phasing [note: this resembles (N, Nb) = (32, 1) design] 2W1: i₁ = 0, 2, 4, 6, 8, 12, 14 4 bits W2: For each W1, choose only (Y1,Y2) = (e1, e1) with all 2 possible co-phasing

TABLE 22 Relationship between the Relationship between the first PMIvalue and second PMI value and codebook index i₁ codebook index i₂ Valueof the Value of the first PMI Codebook second PMI Codebook Total RII_(PMI1) index i₁ I_(PMI2) index i₁ bits 1 0-7 2I_(PMI1) 0-1 2I_(PMI2) 42 0-7 2I_(PMI1) 0-1 I_(PMI2) 4

For PUCCH mode 2-1, the same sub-sampling table and PUCCH format for 8Txcan be used for 4Tx.

Rank-3/4

For a UE capable of 4-layer operation, PUCCH sub-sampling depends on thecodebook design for rank-3/4.

If rank-3/4 of the enhanced 4Tx codebook reuses the LTE Release 8codebook, PUCCH sub-sampling shall consider the fact that only onewideband W1 is available for rank-3 and rank-4 (e.g., 4×4 identitymatrix). Therefore, the PUCCH sub-sampling Tables 23 and 24 should beused.

TABLE 23 Number of W1 RI Chosen W1 index for sub-sampling (i₁)hypotheses 1 Every other W1 matrix of the GoB 8 codebook, e.g. 0 = 0, 2,4, 6, 8, 10, 12, 14 2 Every other W2 matrix of the GoB 8 codebook, e.g.0 = 0, 2, 4, 6, 8, 10, 12, 14 3 LTE Release 8 codebook, i.e., i₁ = 0 1 4LTE Release 8 codebook, i.e., i₁ = 0 1 Total number of hypotheses acrossranks: 16 → 4 bits for UE capable of 2-layers 18 → 5 bits for UE capableof 4-layers

TABLE 24 Value of joint encoding of RI and the first PMI CodebookIRI/PM_(I1) RI index i₁ 0-7 1 2I_(RI/PMI1)  8-15 2 2(I_(RI/PMI1) − 8) 16 3 2(I_(RI/PMI1) − 16) 17 4 2(I_(RI/PMI1) − 17) 17-31 reserved NA

Similarly for PUCCH submode 2 where W1 is jointly encoded with W2/CQI,for a UE capable of 4-layer transmission, PUCCH sub-sampling shallconsider the fact only one wideband W1 is available for rank-3 andrank-4 (e.g. an identity matrix). Tables 25 and 26 are an example ofsuch sub-sampling.

TABLE 25 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 W1: 0, 2, 4, 6, 8, 10, 12, 14 (i₁) 8 * 16 = 64 → 7 bits W2:For each W1 (i₁ = 0, 1, 2, 3), choose Y = e₁, e₂, e₃, e₄ with all 4possible co-phasing. (Note this resembles (N, Nb) = (32, 1) design.) 2W1: i₁ = 0, 2, 4, 6, 8, 12, 14 4 bits W2: For each W1, choose only (Y₁,Y₂) = (e₁, e₁) with all 2 possible co-phasing. 3 W1: i₁ = 0 (e.g., theLTE Release 8 4 bits codebook is chosen, W1 = I₄). W2: no sub-sampling.3 W1: i₁ = 0 (e.g., the LTE Release 8 4 bits codebook is chosen, W1 =I₄). W2: no sub-sampling.

TABLE 26 Relationship between the Relationship between the first PMIvalue and second PMI value and codebook index i₁ codebook index i₂ Valueof the Value of the first PMI Codebook second PMI Codebook Total RII_(PMI1) index i₁ I_(PMI2) index i₂ bits 1 0-7 2I_(PMI1) 0-1  2I_(PMI2)4 2 0-7 2I_(PMI1) 0-1  I_(PMI2) 4 3 0 0 0-15 I_(PMI2) 4 4 0 0 0-15I_(PMI2) 4

Sub-Sampling for Other Codebooks.

A hybrid codebook is proposed in pending U.S. patent application Ser.No. 14/177,547.

Sub-sampling for this codebook should following a few high-levelprinciples.

-   -   The sub-sampled codebook should comprise W1 matrices with both        adjacent beams and distributed beams. W1 with adjacent beams are        advantageous in channels with narrow angular spread, and/or with        perfecting antenna calibration. On the other hand, W1 with        distributed beams are more suitable for channel with large        antenna spacing, with wide angular spread, or with timing        misalignment error at the eNB.    -   For W1 matrices with adjacent beams, different W1 matrices with        overlapping beams are not necessary because the edge effect is        not significant for wideband PMI feedback on PUCCH. Therefore,        sub-sampled W1 should include W1 without overlapping.    -   For W1 matrices with distributed beams, note that there are a        total of 8 W1 matrices, each offset by one DFT beam of an        over-sampling rate N=32. Sub-sampled codebook may use every        second W1 matrix, or every fourth W1 matrix, depending on the        overhead payload after sub-sampling.

For PUCCH mode 1-1, submode 1, the sub-sampling possibilitiesillustrated in Tables 27 and 28 are proposed.

TABLE 27 Number of W1 RI Chosen W1 index for sub-sampling (i₁)hypotheses 1 Every other W1 matrix of the GoB 8 codebook, e.g. i₁ = 0,2, 4, 6, 8, 10, 12, 14 2 Every other W2 matrix of the GoB 8 codebook,e.g. i₁ = 0, 2, 4, 6, 8, 10, 12, 14 3 Use LTE Release 8 codebook, 1i.e., i₁ = 0 4 Use LTE Release 8 codebook, 1 i.e., i₁ = 0 Total numberof hypotheses across ranks: 16 → 4 bits for UE capable of 2-layers 18 →5 bits for UE capable of 4-layers

TABLE 28 Value of joint encoding of RI and the first PMI CodebookI_(RI/PMI1) RI index i₁ 0-7 1 2I_(RI/PMI1)  8-15 2 2(I_(RI/PMI) − 8)  163 2(I_(RI/PMI) − 16) 17 4 2(I_(RI/PMI) − 17) 17-31 reserved NA

For PUCCH mode 1-1, submode 2, the sub-sampling possibilities in Table29 are proposed.

TABLE 29 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 W1: 0, 2, 4, 6, 8, 10, 12, 14 (i₁) 8 * 16 = 64 → 7 bits W2:For each sub-sampled W1, choose Y = e₁, e₂, e₃, e₄ with all 4 possibleco-phasing. 2 W1: i₁ = 0, 2, 4, 6, 8, 12, 14 4 bits W2: For W1 ofadjacent beams, choose only (Y₁, Y₂) = (e₁, e₁) with all 2 possibleco-phasing W2: For W1 of distributed beams: Embodiment 1:${{choose}\mspace{14mu}{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}}},{{or}\mspace{14mu}{arbitrary}\mspace{14mu}{matrix}}$${{in}\mspace{14mu} C\; 2},{{{and}\mspace{14mu}\left( {Y_{1},Y_{2}} \right)} = {\left\{ {\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{3}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{4}} \right)} \right\}.}}$Embodiment 2: ${{{choose}\mspace{14mu} W\; 2} = {\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}\mspace{14mu}{{and}\mspace{14mu}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}}}},{{{and}\left( {Y_{1},Y_{2}} \right)} = \left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{2}} \right)},{{or}\mspace{14mu}{\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{4}} \right).}}$Embodiment 3: $\;{{{{choose}\mspace{14mu} W\; 2} = \begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{{and}\mspace{14mu}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {jY}_{2}\end{bmatrix}},{{{and}\left( {Y_{1},Y_{2}} \right)} = \left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{3}} \right)},{{or}\mspace{14mu}{\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{4}} \right).}}}$3 W1: i₁ = 0 (e.g., the LTE Release 8 codebook 4 bits is chosen, W1 =I₄) W2: no sub-sampling. 4 W1: i₁ = 0 (e.g., the LTE Release 8 codebook4 bits is chosen, W1 = I₄) W2: no sub-sampling.

PUCCH Mode 2-1 for 4Tx

If PUCCH mode 2-1 is to be supported for the new 4 tx codebook, thePUCCH reporting structure and sub-sampling needs to be studied takinginto account the codebook design of rank-1/2 and rank-3/4.

First we review the reporting structure of PUCCH mode 2-1:

-   -   W is determined from a 3-subframe report conditioned upon the        latest RI report.    -   Reporting format:        -   Report 1 (Type 6): RI and 1-bit precoder type indication            (PTI)        -   Report 2:            -   PTI=0: W1 will be reported (Type 2a)            -   PTI=1: wideband CQI and wideband W2 will be reported                (Type 2b)        -   Report 3:            -   PTI=0: wideband CQI and wideband W2 will be reported                (Type 2b)            -   PTI=1: subband CQI, subband W2 (Type 1a), plus an L-bit                (e.g., L=2) indicator signaling a selected subset of                subbands for which the reported subband CQI/W2 shall                apply.

Given the maximum 11-bit payload of the PUCCH channel, the total numberof CSI bits on each PUCCH transmission shall satisfy the followingconstraint:

-   -   Type 6: 3-bit joint encoding of RI and PTI, no sub-sampling is        needed.    -   Type 2a: wideband W1 (4-bit for rank-1/2, 0-bit if the LTE        Release 8 codebook is used for rank-3/4), no sub-sampling is        needed.    -   Type 2b: wideband W1 (4-bit for rank-1/2, 0-bit if the LTE        Release 8 codebook is used for rank-3/4) and CQI (4-bit for        rank-1 and 7-bit for rank>1), no sub-sampling is needed.    -   Type 1a: subband W2+subband CQI (4-bit for rank-1 and 7-bit for        rank>1)+L (e.g., L=2) bits subband indicator.        -   Rank1: subband W2 payload is 4 bits.        -   Rank>1: subband W2 payload is 2 bits.

As can be seen, sub-sampling is only required for PUCCH type 1a. This isdiscussed in the following.

Rank-1/2

For rank-1/2, if the same GoB framework and parameters of 8Tx are usedto design the 4Tx codebook, the W1/W2 codebook size of 4Tx will beexactly the same as of 8Tx. In brief, the W1 wideband precoder is 4bits, while W2 precoder is also 4 bits. As such, the sub-samplingdetails of PUCCH mode 2-1 for 8Tx can be reused without any change for4Tx.

Table 30 illustrates PUCCH mode 2-1, type 1a sub-sampling for rank-1/2.

TABLE 30 Relationship between the second PMI value and codebook index i₂Value of the Codebook RI second PMI I_(PMI2) index i₂ 1 0-15 I_(PMI2) 20-3  2I_(PMI2)

Rank-3/4

For rank-3/4, the LTE Release 8 codebook is preferably reused becauseGoB codebook does not bring significant performance improvement, or evencauses performance degradation in some scenarios. The W1 codebook has0-bit (e.g., a single element of a 4×4 identity matrix), and the W2codebook reuses the LTE Release 8 codebook which is 4 bits. As a result,sub-sampling for 4Tx PUCCH mode 2-1 needs to be redesigned for rank-3/4,to reduce W2 to 2-bit.

To solve this issue we take a closer look at the LTE Release 8 codebookstructure. The LTE Release 8 codebook satisfies the nested propertywhere the l-th precoder (l=0, . . . 15) of rank r (r=1, 2, 3, 4)comprises 1 columns of the Householder transformation of the l-th 4x1base vector. Furthermore, the rank-1 LTE Release 8 codebook consists ofsixteen vectors (e.g., 4 bits), where the first eight vectors are DFTvectors which are preferably used for uniform linear array (ULA)antennas at the eNB, and the last eight vectors are optimized forcross-polarized (XPD) antenna configuration at the eNB. The phase ofeach 4Tx Rel-8 rank-1 codebook is tabularized below.

Table 31 is an analysis of the phase of the rank-1 LTE Release 8codebook.

TABLE 31 Precoder index 0 1 2 3 4 5 6 7 Antenna-1$0 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ $1 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$ Antenna2$0 \times \frac{\pi}{2}$ $1 \times \frac{\pi}{2}$$2 \times \frac{\pi}{2}$ $3 \times \frac{\pi}{2}$$0.5 \times \frac{\pi}{2}$ $1.5 \times \frac{\pi}{2}$$2.5 \times \frac{\pi}{2}$ $3.5 \times \frac{\pi}{2}$ Antenna 3$0 \times \frac{\pi}{2}$ $2 \times \frac{\pi}{2}$$4 \times \frac{\pi}{2}$ $6 \times \frac{\pi}{2}$$1 \times \frac{\pi}{2}$ $3 \times \frac{\pi}{2}$$5 \times \frac{\pi}{2}$ $7 \times \frac{\pi}{2}$ Antenna 4$0 \times \frac{\pi}{2}$ $3 \times \frac{\pi}{2}$$6 \times \frac{\pi}{2}$ $9 \times \frac{\pi}{2}$$1.5 \times \frac{\pi}{2}$ $4.5 \times \frac{\pi}{2}$$7.5 \times \frac{\pi}{2}$ $105 \times \frac{\pi}{2}$ Precoder index 8 910 11 12 13 14 15 Antenna-1 $0 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ Antenna2 $0 \times \frac{\pi}{2}$$1 \times \frac{\pi}{2}$ $2 \times \frac{\pi}{2}$$3 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ $2 \times \frac{\pi}{2}$$2 \times \frac{\pi}{2}$ Antenna 3 $2 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ $2 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$$2 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$$2 \times \frac{\pi}{2}$ Antenna 4 $2 \times \frac{\pi}{2}$$1 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$$3 \times \frac{\pi}{2}$ $2 \times \frac{\pi}{2}$$0 \times \frac{\pi}{2}$ $0 \times \frac{\pi}{2}$$2 \times \frac{\pi}{2}$

It can be seen that the first 8 rank-1 precoders correspond to DFTvectors of beam directions

$\left\{ {0,1,2,3,0.5,1.5,2.5,3.5} \right\} \times {\frac{\pi}{2}.}$These DFT vectors are evenly distributed to provide a uniform coverageof the [0, 2π] degree angle-of-arrival/departure subspace, and areparticularly suitable to be used for ULA antenna arrays. The next 8rank-1 precoders are not DFT vectors and cannot be represented by aspecific angle-of-arrival/departure; however, they can be interpreted asthe spatial signature for a cross-polarized antenna array, where the1^(st) cross-polarization angle (e.g. antenna 1 and antenna 2) and the2^(nd) cross-polarization angle (e.g. antenna 3 and 4) are representedby two separate 2Tx DFT vectors, respectively. Since the rank-3/4codebooks sub-matrices of Housholder transformation of eachcorresponding rank-1 base vector, it is proposed that sub-sampling ofthe rank-3/4 codebook is based on the co-phasing structure of thecorresponding rank-1 codebook. The sub-sampling illustrated in Table 32is proposed for PUCCH type 1a in 4Tx rank-3/4.

Embodiment 1

In one embodiment, for rank-3 and rank-4, the 2-bit sub-sampled W2codebook takes every fourth entry in the LTE Release 8 codebook, e.g.W2: i₂={0, 4 8, 12}+k. Here k is an offset number. An example is givenin Table 31 where k=0 is assumed.

TABLE 32 Number of W2 RI W2 sub-sampling hypothesis 3 W1: i₁ = 0 (e.g.,the LTE Release 8 2 bits codebook is chosen, W1 = I₄). W2: i₂ = 0, 4 8,12 4 W1: i₁ = 0 (e.g. LTE Release 8 2 bits codebook is chosen, W1 = I₄).W2: i₂ = 0, 4 8, 12

Embodiment 2

In another embodiment, for rank-3 and rank-4, the 2-bit sub-sampled W2codebook takes the first four entries in the LTE Release 8 codebook,e.g., W2: i₂=0, 1 2, 3. These are critically sampled DFT vectors thatuniformly quantizes the 4Tx DFT precoding subspace, and are expected towork well for base stations equipped with uniform linear array (ULA)antennas. Alternatively, W2: i₂=4, 5 6, 7 may be considered.

Embodiment 3

In another embodiment, for rank-3 and rank-4, the 2-bit sub-sampled W2codebook takes precoders 8-11 in the LTE Release 8 codebook, e.g., i₂=8,9, 10, 11. These precoders are expected to work well for cross-polarized(XPOL) antenna configurations.

Embodiment 4

In yet another embodiment, for rank-3 and rank-4, the 2-bit sub-sampledW2 codebook takes two W2 precoders from Embodiment 2 (e.g., i2=0, 2) andtwo precoders from Embodiment 3 (e.g., i₂=8, 10). The first two W2precoders are DFT vectors suitable for ULA antenna configuration, andthe next two W2 precoders are non-DFT vectors suitable for XPD antennaconfiguration. This achieves a balanced performance between ULA and XPOLantenna configurations, regardless of the actual antenna configurationthat an eNB deploys.

Embodiment 5

In yet another embodiment, for rank-3 and rank-4, the 2-bit sub-sampledW2 codebooks are configured semi-statically by RRC-higher-layer signals.If a UE is configured in coordinated multi-point (CoMP) transmissionmode and configured with multiple CSI-processes, the RRC configurationof sub-sampled W2 codebook is performed independently per CSI-RSprocess.

It is possible for eNB to semi-statically RRC configure the sub-samplingschemes of PUCCH type 1a for rank-3/4 (e.g., using Embodiment 1 to 5).

Sub-Sampling with Other Codebook Designs.

Several other rank-1/2 4Tx codebooks are possible. This section liststwo possible rank-1/2 4Tx codebooks and discusses their sub-samplingdetails for PUCCH mode 1-1, submode-1, PUCCH mode 1-1 submode 2, andPUCCH mode 2-1.

Alternative Codebook 1

One possible 4Tx codebook for rank-1/2 is listed below, where W1 has 4bits, and W2 has 4 bits.

$\begin{matrix}{{W_{1} = {{\begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}\mspace{14mu}{where}\mspace{14mu} n} = 0}},1,\ldots\mspace{14mu},15} & (35) \\{X_{n} = {{\begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}\mspace{14mu}{where}\mspace{14mu} q_{1}} = e^{j\; 2\;{\pi/32}}}} & (36)\end{matrix}$

For rank 1,

$\begin{matrix}{{W_{2,n} \in \left\{ {{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y_{1} \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\{j{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\ \begin{bmatrix}Y \\{{- j}{\alpha(i)}Y}\end{bmatrix}}} \right\}},} & (37) \\{\mspace{79mu}{{Y \in \left\{ {e_{1},e_{2},e_{3},e_{4}} \right\}},{and}}} & (38) \\{\mspace{79mu}{{\alpha(i)} = q_{1}^{2{({i - 1})}}}} & (39)\end{matrix}$where α(i) is a co-phasing vector.

For rank 2,

$\begin{matrix}{\mspace{79mu}{{W_{2,n} \in \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (40) \\{\left( {Y_{1},Y_{2}} \right) = {\left( {e_{i},e_{k}} \right) \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)} \right\}}} & (41)\end{matrix}$

Note that the n-th W1 matrix (n=0, . . . 15) comprises four distributedDFT beams that cover a wide angular spread. Furthermore, DFT beams indifferent W1 matrices are cyclically shifted. It is noted that the firsteight W1 matrices (n=0, . . . 7) has no overlapping DFT beams, while thelast eight W1 matrices (n=8, . . . 15) comprise exactly the same set ofDFT beams as W1 (n=0, . . . 7) which are cyclically shifted. Hence, ifsub-sampling is needed for W1, the first eight W1 matrices (n=0, . . .7) or a subset thereof shall be used, while the last eight W1 matrices(n=8, . . . 15) can be omitted.

PUCCH Mode 1-1, Submode 1.

In submode 1 where RI/W1 is jointly encoded, sub-sampling is not neededfor W2, but needed for jointly encoded RI/W1. The details depend on themaximum number of bits allowed for jointly encoded RI/W1. In oneembodiment, the number of bits for RI/W1 is 4 bits for a 2-layer UE and5 bits for a 4-layer UE, where sub-sampling details are given in Tables33 and 34

TABLE 33 Number of W1 RI Chosen W1 index for sub-sampling (i₁)hypotheses 1 Eight W1 matrices without overlapping 8 DFT beams, e.g., i₁= {0, 1, . . . 7}. 2 Eight W1 matrices without overlapping 8 DFT beams,e.g., i₁ = {0, 1, . . . 7}. 3 LTE Release 8 codebook, i.e., i₁ = 0 1 4LTE Release 8 codebook, i.e., i₁ = 0 1 Total no. hypotheses acrossranks: 16 → 4 bits for UE capable of 2-layers 18 → 5 bits for UE capableof 4-layers

TABLE 34 Value of joint encoding of RI and the first PMI CodebookI_(RI/PMI) RI index i₁ 0-7 1 I_(RI/PMI)  8-15 2 (I_(RI/PMI) − 8)  16 3(I_(RI/PMI) − 16) 17 4 (I_(RI/PMI) − 17) 18-31 reserved NA

In another embodiment, the number of bits for RI/W1 is 5 bits for a2-layer UE and 6 bits for a 4-layer UE. In this case there is nosub-sampling for RI/W1 or W2/CQI, and the bitfields are given in Tables35 and 36.

TABLE 35 Number of W1 RI Chosen W1 index for sub-sampling (i₁)hypotheses 1 No sub-sampling, e.g., i₁ = 0-15 16 2 No sub-sampling,e.g., i₁ = 0-15 16 3 LTE Release 8 codebook, i.e., i₁ = 0 1 4 LTERelease 8 codebook, i.e., i₁ = 0 1 Total no. hypotheses across ranks: 32→ 5 bits for UE capable of 2-layers 34 → 6 bits for UE capable of4-layers

TABLE 36 Value of joint encoding of RI and the first PMI CodebookI_(RI/PMI) RI index i₁  0-15 1 I_(RI/PMI) 16-31 2 I_(RI/PMI) − 16 32 3I_(RI/PMI) − 32 33 4 I_(RI/PMI) − 33 34-63 reserved NA

If the maximum payload of RI/W1 is a concern, the number of bits forRI/W1 can be reduced to 3 bits for a 2-layer UE and 4 bits for a 4-layerUE. In this case, every second W1 matrix is sub-sampled for rank-1/2.The sub-sampling details are given in Tables 37 and 38.

TABLE 37 Number of W1 RI Chosen W1 index for sub-sampling (i₁)hypotheses 1 Every second of the first eight W1 4 matrices e.g., i₁ ={0, 2, 4, 6}. 2 Every second of the first eight W1 4 matrices, e.g., i₁= {0, 2, 4, 6}. 3 LTE Release 8 codebook, i.e., i₁ = 0 1 4 LTE Release 8codebook, i.e., i₁ = 0 1 Total no. hypotheses across ranks: 8 → 3 bitsfor UE capable of 2-layers 10 → 4 bits for UE capable of 4-layers

TABLE 38 Value of joint encoding of RI and the first PMI CodebookI_(RI/PMI1) RI index i₁ 0-3 1 2I_(RI/PMI) 4-7 2 2(I_(RI/PMI) − 4) 8 3I_(RI/PMI) − 8 9 4 I_(RI/PMI) − 9 10-15 reserved NA

PUCCH Mode 1-1, Submode 2.

For submode 2, W1/W2 and CQI are jointly encoded in a single PUCCHtransmission. Therefore, W1/W2 total payload is limited by 7 bits inrank-1, and 4 bits in rank-2. The sub-sampling schemes illustrated inTable 39 can be considered for PUCCH mode 1-1, submode 2.

TABLE 39 Number of W1 + W2 RI Chosen W1 + W2 index for sub-samplinghypotheses 1 For W1, sub sampling can be 0, 1, . . . 7 (i₁) Max 7 bitsFor W2: either no sub-sampling (e.g., 4-bit W2), or W2 is sub-sampled to3-bits as $W_{2,n} \in \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}$and  Y = e_(i) ∈ {e₁, e₃}  or  Y ∈ {e₂, e₄}  and  α(i) = q₁^(2(i − 1));2 Embodiment 1: 4 bits For W1, sub-sampling can be 0, 1, . . . 7 (i₁)For W2, sub-sampling can be$W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}$ and  (Y₁, Y₂) = (e_(i), e_(k)) ∈ {(e₁, e₁)}Embodiment 2: For W1, sub-sampling can be 0, 2, 4, 6 (i₁)$W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}$and  (Y₁, Y₂) = (e_(i), e_(k)) ∈ {(e₁, e₁), (e₃, e₃)} Embodiment 3: ForW1, sub-sampling can be 0, 4, (i₁)$W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}$and  (Y₁, Y₂) = (e_(i), e_(k)) ∈ {(e₁, e₁), (e₂, e₂)(e₃, e₃), (e₄, e₄)}3 W1: i₁ = 0 (e.g., the LTE Release 8 codebook is chosen, W1 = I₄) 4bits W2: no sub-sampling 4 W1: i₁ = 0 (e.g., the LTE Release 8 codebookis chosen, W1 = I₄) 4 bits W2: no sub-sampling

PUCCH 2-1

Only PUCCH type 1a requires sub-sampling where W2 needs to besub-sampled to 2 bits.

For rank-1, sub-sampled W2 can be

$\begin{matrix}{W_{2,n} \in \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}} & (42) \\{\mspace{85mu}{{{Y \in {\left\{ e_{1} \right\}\mspace{14mu}{and}\mspace{14mu}{\alpha(i)}}} = q_{1}^{2{({i - 1})}}};}} & (43) \\{\mspace{79mu}{or}} & \; \\{\mspace{79mu}{W_{2,n} \in \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}}} \right\}}} & (44) \\{\mspace{79mu}{{{Y \in {\left\{ {e_{1},e_{3}} \right\}\mspace{14mu}{and}\mspace{14mu}{\alpha(i)}}} = q_{1}^{2{({i - 1})}}};}} & (45)\end{matrix}$

For rank-2, sub-sampled codebook can be

$\begin{matrix}{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}} & (46) \\{\left( {Y_{1},Y_{2}} \right) = {\left( {e_{i},e_{k}} \right) \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{3},e_{3}} \right)} \right\}}} & (47)\end{matrix}$

Alternative Codebook 2

Another possible 4Tx codebook for rank-1/2 is listed below, where W1 has4 bits, and W2 has 4 bits.

$\begin{matrix}{{W_{1} = {{\begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}\mspace{14mu}{where}\mspace{14mu} n} = 0}},1,\ldots\mspace{14mu},15} & (48) \\{X_{n} = {{\begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}\mspace{14mu}{where}\mspace{14mu} q_{1}} = e^{j\; 2\;{\pi/32}}}} & (49)\end{matrix}$

For rank 1,

$\begin{matrix}{{W_{2,n} \in \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},} & (50) \\{\mspace{79mu}{{Y \in \left\{ {e_{1},e_{2},e_{3},e_{4}} \right\}},{and}}} & \; \\{\mspace{79mu}{{\alpha(i)} = q_{1}^{2{({i - 1})}}}} & (51)\end{matrix}$

For rank 2,

$\begin{matrix}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}},} & (52) \\{\mspace{79mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ \left( {e_{2},e_{4}} \right) \right\}},{and}}} & (53) \\{\mspace{79mu}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (54) \\{\mspace{79mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}},{and}}} & (55) \\{\mspace{79mu}{{W_{2,n} \in \left\{ {\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}} \right\}},}} & (56) \\{\mspace{79mu}{\left( {Y_{1},Y_{2}} \right) \in {\left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}.}}} & (57)\end{matrix}$

Again, the last eight W1 matrices (n=8, . . . 15) comprise exactly thesame set of DFT beams as W1 (n=0, . . . 7), but are cyclically shifted.Hence, if sub-sampling is needed for W1, the first eight W1 matrices(n=0, . . . 7) or a subset thereof shall be used, while the last eightW1 matrices (n=8, . . . 15) can be omitted.

PUCCH Mode 1-1, Submode 1.

In submode 1 where RI/W1 is jointly encoded, sub-sampling is needed forRI/W1 of rank-1/2 where the details are dependent on the maximum numberof bits for jointly encoded RI/W1. Since the W1 codebook is the same asthe alternative codebook 1 above (Eqs. 35 and 36), the same sub-samplingscheme as in Tables 33-38 are applicable. Meanwhile, W2 requires nosub-sampling.

PUCCH Mode 1-1, Submode 2.

For submode 2, W1/W2 and CQI are jointly encoded in a single PUCCHtransmission. Therefore, W1/W2 total payload is limited by 7 bits inrank-1, and 4 bits in rank-2.

Rank 1

Since the rank 1 codebook is the same as for the 4Tx codebook candidateshown above in alternative codebook 1, the same sub-sampling scheme asshown in Table 39 can be applied.

Rank 2

For rank-2, W1/W2 needs to be limited to 4 bits. The followingsub-sampling details are possible:

In one embodiment, W1 is sub-sampled to 2 bits (e.g., i₁=0, 2, 4, 6),and W2 is sub-sampled to 2 bits as:

$\begin{matrix}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}},} & (58) \\{\mspace{85mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ \left( {e_{2},e_{4}} \right) \right\}},}} & (59) \\{\mspace{79mu}{or}} & \; \\{\mspace{79mu}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (60) \\{\mspace{85mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{3},e_{3}} \right)} \right\}},}} & (61) \\{\mspace{79mu}{or}} & \; \\{\mspace{79mu}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}},}} & (62) \\{\mspace{79mu}{\left( {Y_{1},Y_{2}} \right) \in {\left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}.}}} & (63)\end{matrix}$

In another embodiment, W1 is sub-sampled to 1 bit (e.g., i₁=0, 4), andW2 is sub-sampled to 3 bits as:

$\begin{matrix}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}},} & (64) \\{\mspace{79mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ \left( {e_{2},e_{4}} \right) \right\}},{and}}} & (65) \\{\mspace{79mu}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (66) \\{\mspace{79mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{3},e_{3}} \right)} \right\}},\mspace{79mu}{or}}} & (67) \\{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}},} & (68) \\{\mspace{79mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ \left( {e_{2},e_{4}} \right) \right\}},{and}}} & (69) \\{\mspace{79mu}{{W_{2,n} \in \left\{ {\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}} \right\}},}} & (70) \\{\mspace{79mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}},}} & (71) \\{\mspace{79mu}{or}} & \; \\{\mspace{79mu}{{W_{2,n} \in \left\{ {\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}} \right\}},}} & (72) \\{\mspace{85mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}},{and}}} & (73) \\{\mspace{79mu}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (74) \\{\mspace{85mu}{\left( {Y_{1},Y_{2}} \right) \in {\left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{3},e_{3}} \right)} \right\}.}}} & (75)\end{matrix}$

In yet another embodiment, W1 is sub-sampled to 3 bits (e.g., i₁=0, 1, .. . 7), and W2 is sub-sampled to 1 bit as

$\begin{matrix}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}}} \right\}},} & (76) \\{{\left( {Y_{1},Y_{2}} \right) \in \left\{ \left( {e_{2},e_{4}} \right) \right\}},} & (77) \\{or} & \; \\{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},} & (78) \\{{\left( {Y_{1},Y_{2}} \right) \in \left\{ \left( {e_{1},e_{1}} \right) \right\}},} & (79) \\{or} & \; \\{{W_{2,n} \in \left\{ {\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}} \right\}},} & (80) \\{\left( {Y_{1},Y_{2}} \right) \in {\left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right)} \right\}.}} & (81)\end{matrix}$

PUCCH Mode 2-1.

Only PUCCH type 1a requires sub-sampling where W2 needs to besub-sampled to 2 bits. In this case, the 2-bit sub-sampled W2 codebookin Section 7.2.2 can be considered, where

$\begin{matrix}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}},} & (82) \\{\mspace{79mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ \left( {e_{2},e_{4}} \right) \right\}},}} & (83) \\{\mspace{79mu}{or}} & \; \\{\mspace{79mu}{{W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (84) \\{\mspace{79mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{3},e_{3}} \right)} \right\}},}} & (85) \\{\mspace{79mu}{or}} & \; \\{\mspace{79mu}{{W_{2,n} \in \left\{ {\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}} \right\}},}} & (86) \\{\mspace{79mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}},}} & (87)\end{matrix}$

Hybrid Rank-1/2 Codebook Design.

Rank-1/2 codebook comprises two components, where W1 structures aredifferent in each component. For the first eight W1 matrices, Xncomprises four adjacent DFT beams with over-sampling rate of N=16. Forthe last eight W1 matrices, Xn comprises four distributed DFT beamsuniformly sampling the [0, 360] angle of arrival sub-space. Thisprovides wider angular spread coverage and may be beneficial to largetiming misalignment error. The W1 codebook therefore can be given by:

$\begin{matrix}{\mspace{79mu}{{i_{1} = 0},1,\ldots\mspace{14mu},{7\text{:}}}} & \; \\{{X^{(i_{1})} \in \left\{ \left\lfloor \begin{matrix}b_{2i_{1}{mod}\; 16} & b_{{({{2i_{1}} + 1})}\;{mod}\; 16} & b_{{({{2i_{1}} + 2})}{mod}\; 16} & b_{{({{2i_{1}} + 3})}{mod}\; 16}\end{matrix} \right\rfloor \right\}},} & (88) \\{\mspace{79mu}{{{b_{n}\left( {m + 1} \right)} = e^{j\frac{2\;\pi\;{mn}}{16}}},{n = 0},1,\ldots\mspace{14mu},15,\mspace{14mu}{m = 0},{.1}}} & (89) \\{\mspace{79mu}{{i_{1} = 8},9,\ldots\mspace{14mu},{15\text{:}}}} & \; \\{{X^{(i_{1})} \in \left\{ \left\lfloor \begin{matrix}b_{{({i_{1} - 8})}\;{mod}\; 32} & b_{{({i_{1} - 8})} + {8\;{mod}\; 32}} & b_{{({i_{1} - 8})} + {16\;{mod}\; 32}} & b_{{({i_{1} - 8})} + {24\;{mod}\; 32}}\end{matrix} \right\rfloor \right\}},} & (90) \\{\mspace{79mu}{{{b_{n}\left( {m + 1} \right)} = e^{j\frac{2\;\pi\;{mn}}{32}}},{n = 0},1,\ldots\mspace{14mu},31,\mspace{14mu}{m = 0},1}} & (91)\end{matrix}$

W2 codebook: Rank-1 (4-bit):

$\begin{matrix}{{{W_{2} \in C_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{jY}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- {jY}}\end{bmatrix}}} \right\}},} & (92) \\{Y \in {\left\{ {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{3},{\overset{\sim}{e}}_{4}} \right\}.}} & (93)\end{matrix}$

W2 codebook: Rank-2 (4-bit):

For W2 corresponding to i₁=0,1, . . . ,7:

$\begin{matrix}{\mspace{79mu}{{W_{2} \in C_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}} & (94) \\{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{1}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{2}} \right),\left( {{\overset{\sim}{e}}_{3},{\overset{\sim}{e}}_{3}} \right),\left( {{\overset{\sim}{e}}_{4},{\overset{\sim}{e}}_{4}} \right),\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{2}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{3}} \right),\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{4}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{4}} \right)} \right\}} & (95)\end{matrix}$

If (3-bit) W2 is preferred, (Y₁, Y₂) can be changed to:(Y ₁ ,Y ₂)∈{({tilde over (e)} ₁ ,{tilde over (e)} ₁),({tilde over (e)} ₂,{tilde over (e)} ₂),({tilde over (e)} ₃ ,{tilde over (e)} ₃),({tildeover (e)} ₄ ,{tilde over (e)} ₄)}.   (96)

For W2 corresponding to i₁=8,9, . . . ,15:

$\begin{matrix}{{{W_{2} \in C_{2}} = \begin{Bmatrix}{{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},} \\{{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {jY}_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}},} \\{{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{- {jY}_{1}} & {jY}_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{- {jY}_{1}} & {- {jY}_{2}}\end{bmatrix}}}\end{Bmatrix}},} & (97) \\{\mspace{79mu}{\left( {Y_{1},Y_{2}} \right) \in {\left\{ {\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{3}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{4}} \right)} \right\}.}}} & (98)\end{matrix}$

If (3-bit) W2 is preferred, the W2 codebook can be changed to:

$\begin{matrix}{\mspace{79mu}{{{W_{2} \in C_{2}} = \begin{Bmatrix}{{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},} \\{{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}}\end{Bmatrix}},}} & (99) \\{\mspace{79mu}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{3}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{4}} \right)} \right\}},}} & (100) \\{\mspace{79mu}{or}} & \; \\{{{W_{2} \in C_{2}} = \begin{Bmatrix}{{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},} \\{{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {jY}_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}},} \\{{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{- {jY}_{1}} & {jY}_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{- {jY}_{1}} & {- {jY}_{2}}\end{bmatrix}}}\end{Bmatrix}},} & (101) \\{\mspace{79mu}{\left( {Y_{1},Y_{2}} \right) \in {\left\{ \left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{3}} \right) \right\}\mspace{14mu}{or}\mspace{14mu}{\left\{ \left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{4}} \right) \right\}.}}}} & (102)\end{matrix}$

Sub-Sampling of Alternative Codebook for 4Tx.

A sub-sampled codebook for PUCCH mode 1-1 submode 2 for transmissionmodes 8, 9 and 10 configured with the alternative codebook for 4Tx isdefined in Table 40 for the first and second precoding matrix indicatori₁ and i₂.

Joint encoding of rank and first precoding matrix indicator i₁ for PUCCHmode 1-1 submode 1 for transmission modes 8, 9 and 10 configured withthe alternative codebook for 4Tx is defined in Table 41.

The sub-sampled codebook for PUCCH mode 2-1 for transmission modes 8, 9and 10 configured with the alternative codebook for 4Tx is defined inTable 42 for PUCCH Reporting Type 1a.

Table 40 illustrates PUCCH mode 1-1 submode 2 codebook subsampling with4 antenna ports.

TABLE 40 Relationship between the Relationship between the first PMIvalue and second PMI value and codebook index i₁ codebook index i₂ Valueof the Value of the first PMI Codebook second PMI Codebook Total RII_(PMI1) index i₁ I_(PMI2) index i₂ bits 1 0-3 4I_(PMI1) 0-3 2I_(PMI2) + 4 · 4 └I_(PMI2)/2┘ 2 0-3 4I_(PMI1) 0-3  I_(PMI2) + 2 · 4└I_(PMI2)/2┘ 3 0 0 0-15 I_(PMI2) 4 4 0 0 0-15 I_(PMI2) 4

Table 41 illustrates joint encoding of RI and for PUCCH mode 1-1 submode1 with 4 antenna ports.

TABLE 41 Value of joint encoding of RI and the first PMI CodebookI_(RI/PMI1) RI index i₁ 0-7 1 I_(RI/PMI1)  8-15 2 I_(RI/PMI1) − 8 16 3 017 4 0 18-31 reserved NA

Table 42 illustrates PUCCH mode 2-1 codebook subsampling with 4 antennaports.

TABLE 42 Relationship between the second PMI value and codebook index i₂Value of the Codebook RI second PMI I_(PMI2) index i₂ 1  0-15 I_(PMI2) 20-3 I_(PMI2) + 2 · └I_(PMI2)/2┘ 3 0-3 2I_(PMI2) +4 · └I_(PMI2)/2┘ 4 0-32I_(PMI2) + 4 · └I_(PMI2)/2┘

FIG. 3 is a block diagram illustrating internal details of a mobile UE301 and an eNB 302 in the network system of FIG. 1. Mobile UE 301 mayrepresent any of a variety of devices such as a server, a desktopcomputer, a laptop computer, a cellular phone, a Personal DigitalAssistant (PDA), a smart phone or other electronic devices. In someembodiments, the electronic mobile UE 301 communicates with eNB 302based on a LTE or Evolved Universal Terrestrial Radio Access Network(E-UTRAN) protocol. Alternatively, another communication protocol nowknown or later developed can be used.

Mobile UE 301 comprises a processor 303 coupled to a memory 304 and atransceiver 305. The memory 304 stores (software) applications 306 forexecution by the processor 303. The applications could comprise anyknown or future application useful for individuals or organizations.These applications could be categorized as operating systems (OS),device drivers, databases, multimedia tools, presentation tools,Internet browsers, emailers, Voice-Over-Internet Protocol (VOIP) tools,file browsers, firewalls, instant messaging, finance tools, games, wordprocessors or other categories. Regardless of the exact nature of theapplications, at least some of the applications may direct the mobile UE301 to transmit UL signals to eNB (base-station) 302 periodically orcontinuously via the transceiver 305. In at least some embodiments, themobile UE 301 identifies a Quality of Service (QoS) requirement whenrequesting an uplink resource from eNB 302. In some cases, the QoSrequirement may be implicitly derived by eNB 302 from the type oftraffic supported by the mobile UE 301. As an example, VOIP and gamingapplications often involve low-latency uplink (UL) transmissions whileHigh Throughput (HTP)/Hypertext Transmission Protocol (HTTP) traffic caninvolve high-latency uplink transmissions.

Transceiver 305 includes uplink logic which may be implemented byexecution of instructions that control the operation of the transceiver.Some of these instructions may be stored in memory 304 and executed whenneeded by processor 303. As would be understood by one of skill in theart, the components of the uplink logic may involve the physical (PHY)layer and/or the Media Access Control (MAC) layer of the transceiver305. Transceiver 305 includes one or more receivers 307 and one or moretransmitters 308.

Processor 303 may send or receive data to various input/output devices309. A subscriber identity module (SIM) card stores and retrievesinformation used for making calls via the cellular system. A Bluetoothbaseband unit may be provided for wireless connection to a microphoneand headset for sending and receiving voice data. Processor 303 may sendinformation to a display unit for interaction with a user of mobile UE301 during a call process. The display may also display picturesreceived from the network, from a local camera, or from other sourcessuch as a Universal Serial Bus (USB) connector. Processor 303 may alsosend a video stream to the display that is received from various sourcessuch as the cellular network via RF transceiver 305 or the camera.

During transmission and reception of voice data or other applicationdata, transmitter 307 may be or become non-synchronized with its servingeNB. In this case, it sends a random access signal. As part of thisprocedure, it determines a preferred size for the next datatransmission, referred to as a message, by using a power threshold valueprovided by the serving eNB, as described in more detail above. In thisembodiment, the message preferred size determination is embodied byexecuting instructions stored in memory 304 by processor 303. In otherembodiments, the message size determination may be embodied by aseparate processor/memory unit, by a hardwired state machine, or byother types of control logic, for example.

eNB 302 comprises a processor 310 coupled to a memory 311, symbolprocessing circuitry 312, and a transceiver 313 via backplane bus 314.The memory stores applications 315 for execution by processor 310. Theapplications could comprise any known or future application useful formanaging wireless communications. At least some of the applications 315may direct eNB 302 to manage transmissions to or from mobile UE 301.

Transceiver 313 comprises an uplink Resource Manager, which enables eNB302 to selectively allocate uplink Physical Uplink Shared CHannel(PUSCH) resources to mobile UE 301. As would be understood by one ofskill in the art, the components of the uplink resource manager mayinvolve the physical (PHY) layer and/or the Media Access Control (MAC)layer of the transceiver 313. Transceiver 313 includes at least onereceiver 315 for receiving transmissions from various UEs within rangeof eNB 302 and at least one transmitter 316 for transmitting data andcontrol information to the various UEs within range of eNB 302.

The uplink resource manager executes instructions that control theoperation of transceiver 313. Some of these instructions may be locatedin memory 311 and executed when needed on processor 310. The resourcemanager controls the transmission resources allocated to each UE 301served by eNB 302 and broadcasts control information via the PDCCH.

Symbol processing circuitry 312 performs demodulation using knowntechniques. Random access signals are demodulated in symbol processingcircuitry 312.

During transmission and reception of voice data or other applicationdata, receiver 315 may receive a random access signal from a UE 301. Therandom access signal is encoded to request a message size that ispreferred by UE 301. UE 301 determines the preferred message size byusing a message threshold provided by eNB 302. In this embodiment, themessage threshold calculation is embodied by executing instructionsstored in memory 311 by processor 310. In other embodiments, thethreshold calculation may be embodied by a separate processor/memoryunit, by a hardwired state machine, or by other types of control logic,for example. Alternatively, in some networks the message threshold is afixed value that may be stored in memory 311, for example. In responseto receiving the message size request, eNB 302 schedules an appropriateset of resources and notifies UE 301 with a resource grant.

Many modifications and other embodiments of the invention(s) will cometo mind to one skilled in the art to which the invention(s) pertainhaving the benefit of the teachings presented in the foregoingdescriptions, and the associated drawings. Therefore, it is to beunderstood that the invention(s) are not to be limited to the specificembodiments disclosed. Although specific terms are employed herein, theyare used in a generic and descriptive sense only and not for purposes oflimitation.

The invention claimed is:
 1. A method comprising: transmitting, by auser equipment, a channel state information (CSI) feedback signalhaving: a first report jointly coding a Rank Indicator (RI) and a firstprecoding matrix indicator (PMI1) associated with the index of a firstprecoding matrix (W1), and a second report coding a Channel QualityIndicator (CQI) and a second precoding matrix indicator (PMI2)associated with the index of a second precoding matrix (W2), and whereinjointly coding the RI and the PMI1 employs codebook sub-sampling asfollows: Value of joint encoding Chosen W1 index of RI and the first PMIfor sub-sampling (I_(RI/PMI1)) RI (i₁) 0-7 1 I_(RI/PMI1)  8-15 2I_(RI/PMI1) − 8 16 3 0 17 4 0 18-31 reserved NA.


2. The method in claim 1, wherein: sub-sampling of PMI1 skips W1matrices with overlapping beams.
 3. A method comprising: transmitting,by a user equipment, a channel state information (CSI) feedback signalhaving: a first report coding a Rank Indicator (RI), and a second reportcoding a first precoding matrix indicator (PMI1) associated with theindex of a first precoding matrix (W1), a second precoding matrixindicator (PMI2) associated with the index of a second precoding matrix(W2), and a Channel Quality Indicator (CQI), and wherein coding the PMI2employs codebook sub-sampling as follows, for RI=1 and 2: Relationshipbetween the second PMI value and W2 index (i₂) Value of the Chosen W2index second PMI for sub-sampling RI (I_(PMI2)) (i₂) 1 0-3 2I_(PMI2) + 4· └I_(PMI2)/2┘ 2 0-3 I_(PMI2) + 2 · └I_(PMI2)/2┘.


4. A method comprising: transmitting, by a user equipment, a channelstate information (CSI) feedback signal having: a first report coding aRank Indicator (RI), and a second report coding a first precoding matrixindicator (PMI1) associated with the index of a first precoding matrix(W1), a second precoding matrix indicator (PMI2) associated with theindex of a second precoding matrix (W2), and a Channel Quality Indicator(CQI), and wherein coding the PMI2 employs codebook sub-sampling asfollows, for RI=3 and 4: Relationship between the second PMI value andW2 index (i₂) Value of the Chosen W2 index second PMI for sub-samplingRI (I_(PMI2)) (i₂) 3 0-15 I_(PMI2) 4 0-15 I_(PMI2).